I may be way off base here, but that question seems kind of like "Should I use a chainsaw or a motorcycle?" to me... The answer depends on what you want to do, but the tools are definitely NOT interchangable in my mind!
As you pointed out, Microsoft Access is very good at managing lists. If you think of projects in terms of resources, tasks, and assignments, then Access would be my tool of choice.
Microsoft Project is good at dealing with tasks, deadlines, resource management and project management. Project provides more finished tools in terms of professionally built data entry and reporting packages.
If MS-Project does everything that you need, it will do those things faster and easier than MS-Access could do them. If MS-Project falls short of your needs and you are willing to invest some time into learning to use MS-Access, you can build almost anything using MS-Access and once you've built something you can customize it just as easily.
MS-Project offers you something akin to the toy truck built the way that the factory thought it should be built. Access takes more time up front, but it offers you something akin to legos for making a truck the way you think a truck ought to be built. Different approaches, both get you your toy truck, but those trucks aren't exactly the same.
-PatP